
Type I ("Big Rip") : In this case, the scale factor , effective energy density and effective pressure density diverges. This is a scenario of universal death, wherein everything which resides in the universe is progressively torn apart [1]}.

Type II ("Sudden/Quiescent singularity") : In this case, the pressure density diverges and so does the derivatives of the scalar factor from the second derivative onwards. The weak and strong energy conditions hold for this singularity. Also known as quiescent singularities, but this name originally appeared in contexts related to non-oscillatory singularities [2]}. A special case of this is the big brake singularity [3]}.

Type III ("Big Freeze") : In this case, the derivative of the scale factor from the first derivative onwards diverges. These were detected in generalized Chaplygin gas models [4]}.

Type IV ("Generalized sudden singularities"): These are finite time singularities with finite density and pressure instead of diverging pressure. In this case, the derivative of the scale factor diverges from a derivative higher than the second.

Type V ("w-singularities") : In this case, the scale factor, the energy and pressure densities are all finite but the barotropic index \(w = \frac{p}{\rho }\)  becomes singular [5]}.

Type \(\infty \) (" Directional singularities "): Curvature scalars vanish at the singularity but there are causal geodesics along which the curvature components diverge [6]} and in this sense, the singularity is encountered just for some observers.

Inaccessible singularities: These singularities appear in cosmological models with toral spatial sections, due to infinite winding of trajectories around the
tori. For instance, compactifying spatial sections of the de Sitter model to cubic tori. However, these singularities cannot be reached by physically well defined observers and hence this prompts the name inaccessible singularities [7]}.

